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Math Help - Binomial Question

  1. #1
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    Binomial Question

    Given n=10 and p =0.05

    Find n where P(X< n)=0.8

    I have found

    P(X<1) = P(X=0) = 0.599

     P(X<2) = P(X=0)+P(X=1) =0.914

     n \in \mathbb{Z}^+ ?

    So n= 2 ? n cannot be a decimal answer.
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  2. #2
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    Maybe I'm misreading something. How did you calculate this because:

    pr(x<1)=pr(x=0)={{10}\choose{0}}(0.5)^{0}(0.5)^{10  }\approx 0.000977

    Looking at a binomial probability sums table, I can tell you the answer is not 2. I think you need to recheck your math. If you need help, let me know. Thanks.

    Oops! I did misread. I thought p=0.5. My mistake.

    Anyway, the answer should be 1, because it's the closest positive integer answer that doesn't cause the binomial probability to go over 0.8.
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  3. #3
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    Quote Originally Posted by Bushy View Post
    Given n=10 and p =0.05

    Find n where P(X< n)=0.8

    [snip]
    Using the same symbol (n in this case) to mean two different things in a question is dumb and is no doubt contributing to your confusion. Furthermore, the probability will never equal 0.8 for a discrete value but obviously X can only equal discrete values ....

    The question can be repaired (barely) by stating it as follows:

    Quote Originally Posted by Bushy and modified by Mr F
    Given n=10 and p =0.05

    Find x where P(X< x)<0.8

    [snip]
    Using trial and error is a reasonable approach to take but, as the previous poster has said, the answer is not x = 2. In fact, the answer to my edited question is x = 1.
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